ASAXS - Overview

Over the past few years I have been working along side my PhD supervisor (Dr Rudi Winter, UWA), Dr Chris Martin (SRS, Daresbury), and Dr Armin Hoell (HMI & BESSY, Berlin) to develop the complex experimental procedure of anomalous small-angle x-ray scattering (ASAXS) to experiments conducted in-situ at high temperatures (1000 degC).

PHOTO RIGHT: The on-line furnace mounted on beamline 7T-MPW-SAXS at BESSY.

Small Angle X-ray Scattering (SAXS) has been used for many years to study the morphology of complex materials. Using SAXS it is possible to obtain the shape and size distribution of the sample parts providing the electron contrast. ASAXS uses an elements absorption edge to create an element specific contrast within the obtained scattering pattern. By using energies close to an elements absorption edge, one must modify the electron contrast by the inclusion of an energy dependent complex correction factor.

The scattered intensity is proportional to the square of the electron density difference

Near the absorption edge, the energy dependent complex correction causes the scattered intensity to be

As one can easily see, the scattered intensity has now got three parts, known as the normal, the cross and the resonant scattering terms. The normal scattering is the same scattering as would be obtained whilst conducting an simple SAXS experiment. The cross and resonant scattering terms describe the correlation between unlike and like (respectively) scattering elements. If one obtains scattering patterns at two carefully chosen energies near the absorption edge and one far below the edge, it is possible (by simple matrix algebra) to obtain theses individual contributions.

PIC LEFT: (A) Shows scattering patterns obtained at the three energies as explained in the text above (the scattering patterns have been shifted vertically for clarity). (B) The three deconvoluted patterns - top normal scattering, middle cross scattering, bottom resonant scattering (again the scattering patterns have been shifted for clarity).

One of the biggest contributors to a poor energy dependent contrast is that of poor choice of energies to be used. Cromer and Lieberman produced some theoretical models for the f ` and f `` of isolated atoms of various elements. These values are tabulated and can be found at various resources on the web. However, in real samples (other than metals) there will be some chemical shift associated with the position of the edge, and also there is a chance of some narrowing / broadening of the resonance lineshape. This is due to the fact that the elements atom is likely to be in close proximity to other elements atoms - for example oxygen. This will modify the electron density in those regions and as such modify the resonance lineshape.

PIC RIGHT: The diagram shows the f `` resonance minimum for the Cromer Lieberman theoretical curve (red) and an alumina-zirconia-silicate nanoceramic (green).

FYI - It is possible to calculate the f `` resonance curve from a simple absorption plot (which is proportional to f `) by using a Kramers-Kronig Difference transformation.

SELECTED PAPERS:

Le Messurier, D., Winter, R., Martin, CM., “In-situ SAXS studies of the morphological changes of an alumina-zirconia-silicate ceramic during its formation”, J.Appl.Cryst., 39, (2006) 598

Winter, R., Le Messurier, D., Martin, CM., “Energy-dependent in-situ small-angle x-ray scattering of nano-ceramics”, Cryst.Rev., 12, (2006) 3

THIS WORK WAS FUNDED BY THE FOLLOWING AGENCIES.